Modelling the change in contact matrices
| timeuse | household |
|---|---|
| weekly | household |
Figure 0.1: Changes in different activities as per the Google mobility data. The google mobility data is provided by local authority. To calculate the activity by region we calculated the mean activity weighted by population for the relevant locations. The different panels match different activities measured by google mobility data.
Figure 0.2: School attendance by age group
Figure 0.3: School attendance by age group
0.1 Interventions
Figure 0.4: Change in dominant eigenvalue value over time by region using the weighted contact matrices.
Figure 0.5: Change in dominant eigenvalue value over time by region using the weighted contact matrices.
Figure 0.6: Short term change in dominant eigenvalue value over time by region using the weighted contact matrices.
0.2 Figures for England
1 2020-04-04 SPIM Scenarios
2 Text and tables for supplementary materials
Time dependent contact matrices are based on location-specific POLYMOD matrices (where locations include at work'',at home'', ``on transport'' etc), combined with the time-use survey. The traditional POLYMOD matrices are used until March, the time of the lockdown. From this point on, the google mobility and time-use survey data are used to calculate proportionate reductions in the location-specific POLYMOD matrices, which are summed together to give a weekly-varying contact matrix, \(\vec{M}^t\)
TODO: talk about different activities
2.1 School attendance
2.2 Home contacts
2.3 Google mobility data
During the pandemic Google provided aggregated mobility data from Android phones for many countries (https://www.google.com/covid19/mobility/). The mobility data gives an indication of the a number of activities: retail and recreation, grocery and pharmacy, parks, transit stations, workplaces and residential. For the United Kingdom this data was provided by different geographical areas. For this study this data was accessed, and matched to local authority area. The data for all local authorities in England were then combined, weighted by population size. Finally, the daily values were averaged by week, to produce weekly activity levels.
2.4 Weekly time use data
(Leeuwen, Group, and Sandmann 2020) used the following derivation to calculate contact weight: \[ \begin{aligned} \kappa_{ial} &=& \frac{w_{ial}t_{ial}}{\sum_b^A w_{ibl} t_{ibl}} \\ k_{ial,j} &=& \kappa_{ial}k_{il,j} \end{aligned} \] with \(\kappa_{ial}\) the activity weight for age group \(i\), activity \(a\) at location \(l\), \(t_{ial}\) is the average time spent by an individual, \(A\) is the set of activities and \(w_{ial}\) is an activity specific weight, which reflects the relative number of people met during this activity compared to other activities at the same location. Most weights will be kept equal to 1 unless specified otherwise.
To account for changes over the year in time spent we added an additional scaling, to scale location contacts with the relative amount spent in those locations. The relative amount of time spent in each location, except for at home, is included as below. \[ \begin{aligned} \kappa_{wial} &=& \frac{t_{wil}}{\overline{t_{wil}}}\frac{w_{ial}t_{wial}}{\sum_b^A w_{ibl} t_{wibl}} \\ t_{wil} &=& \sum_a t_{wial} \\ \overline{t_{wil}} &=& \frac{\sum_w t_{wil}}{|W|} \end{aligned} \] where \(t_{wil}\) is the time spent that week (\(w \in W\)) by stratum \(i\) in location \(l\) and \(\overline{t_{wil}}\) is the time spent by stratum \(i\) in location \(l\) averaged over all weeks. Home contacts are not scaled in this manner, because we assume that more time spent at home does not increase the number of unique contacts at home.
Figure 2.1: Time use by age group changing over time in England
Leeuwen, Edwin van, PHE Joint modelling Group, and Frank Sandmann. 2020. “Augmenting Contact Matrices with Time-Use Data for Fine-Grained Intervention Modelling of Disease Dynamics: A Modelling Analysis.” medRxiv, June. Cold Spring Harbor Laboratory Press, 2020.06.03.20067793. doi:10/gg2bhq.